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Difference between revisions of "Affine hull"

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{{TEX|done}}{{MSC|14R}}
 
{{TEX|done}}{{MSC|14R}}
  
''of a set $M$ in a vector space $V$''
+
''of a [[set]] $M$ in a [[vector space]] $V$''
  
 
The intersection of all flats (translates of subspaces) of $V$ containing $M$.   
 
The intersection of all flats (translates of subspaces) of $V$ containing $M$.   
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It is equal to the set of all finite linear combinations of elements $\{m_i : i=1,\ldots,n \}$ of $M$,
 
It is equal to the set of all finite linear combinations of elements $\{m_i : i=1,\ldots,n \}$ of $M$,
 
$$
 
$$
\sum_{i=1}^n c_i m_i$
+
\sum_{i=1}^n c_i m_i
 
$$
 
$$
 
where the coefficients $c_i$ satisfy
 
where the coefficients $c_i$ satisfy

Revision as of 11:09, 2 May 2016

2020 Mathematics Subject Classification: Primary: 14R [MSN][ZBL]

of a set $M$ in a vector space $V$

The intersection of all flats (translates of subspaces) of $V$ containing $M$.

Comment

It is equal to the set of all finite linear combinations of elements $\{m_i : i=1,\ldots,n \}$ of $M$, $$ \sum_{i=1}^n c_i m_i $$ where the coefficients $c_i$ satisfy $$ \sum_{i=1}^n c_i = 1 \ . $$

References

  • Grünbaum, Branko, Convex polytopes. Graduate Texts in Mathematics 221. Springer (2003) ISBN 0-387-40409-0 1033.52001 Zbl 1033.52001
How to Cite This Entry:
Affine hull. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affine_hull&oldid=38757
This article was adapted from an original article by V.A. Zalgaller (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article